We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm.

Geraci, M., Farcomeni, A. (2020). A family of linear mixed-effects models using the generalized Laplace distribution. STATISTICAL METHODS IN MEDICAL RESEARCH, 29(9), 2665-2682-2682 [10.1177/0962280220903763].

A family of linear mixed-effects models using the generalized Laplace distribution

Farcomeni, Alessio
2020-09-01

Abstract

We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm.
set-2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/01 - STATISTICA
English
Con Impact Factor ISI
Best linear predictor
chi-bar squared
convolution
heterogeneity of treatment effects
longitudinal data
meta-analysis
Geraci, M., Farcomeni, A. (2020). A family of linear mixed-effects models using the generalized Laplace distribution. STATISTICAL METHODS IN MEDICAL RESEARCH, 29(9), 2665-2682-2682 [10.1177/0962280220903763].
Geraci, M; Farcomeni, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/253079
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